{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Derivative of Gaussian Process Regression - 2D\n",
    "\n",
    "高斯过程回归(GPR)的底层在于多元高斯分布良好的解析性。\n",
    "这里我们想进一步考虑回归结果的导数计算。\n",
    "延续前面的 2D-GPR 的标识，我们这里将维度回归一维，\n",
    "基本约定为：用 ti (或者 xi) 和 zi 来表示先验二维数据位置和相应的值，\n",
    "用 tp (或者 xp) 和 zp 来表示要预测的位置和最终的预测值。另外特别需要注意，\n",
    "由于 python 的数据存放机制，我们种类以行向量表示一维数据，而非一般教科书的列向量。\n",
    "并且 zi 的个数为 n，zp 的个数为 m; 均值函数为 $ \\mu_x $\n",
    "\n",
    "$$ \\mu(t_p) = [z_i - \\mu_x(t_i)]_{1,n} \\cdot K^{-1}_{n,n} (t_i, t_i) \\cdot K_{n,m} (t_p, t_i) + \\mu_x(t_p) $$\n",
    "\n",
    "$$ \\sigma^2(t_p) = K_{m,m} (t_p, t_p) - K_{m,n} (t_i, t_p) \\cdot K^{-1}_{n,n} (t_i, t_i) \\cdot K_{n,m} (t_p, t_i) $$\n",
    "\n",
    "如果考虑将 $ \\mu(t_p) $ 对 tp 求导，\n",
    "会发现这里核心需要计算的只有 $ K_{n,m} (t_p, t_i) $ 和 $ \\mu_x(t_p) $ 的关于 tp 的导数。\n",
    "进一步推导不难发现，这里我们实际上可以对每个矩阵元独立求导即可。\n",
    "因此我们为了计算导数，只需要将两者换成相应的矩阵元素导数结果即可。\n",
    "如果取常数的均值函数，其导数即为 0 ，对总的结果没有贡献；\n",
    "对于核函数部分，我们只需要给出原先核函数关于第一项的导数函数即可。\n",
    "下面给出一个具体的例子。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.linalg import solve\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def calc(x):\n",
    "    return x * np.cos(x)\n",
    "\n",
    "def dcalc(x):\n",
    "    return np.cos(x) - x*np.sin(x)\n",
    "\n",
    "xi = np.array([1, 3, 5, 7, 9, 11])\n",
    "zi = calc(xi)\n",
    "plt.scatter(xi, zi)\n",
    "\n",
    "x_real = np.linspace(0, 12, 101)\n",
    "z_real = calc(x_real)\n",
    "dz_real = dcalc(x_real)\n",
    "plt.plot(x_real, z_real)\n",
    "plt.plot(x_real, dz_real)\n",
    "plt.legend(['samples', 'real', 'derivative'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def kernel(u, v, scale):\n",
    "    ug, vg = np.meshgrid(u, v)\n",
    "    return np.exp(-np.power(ug-vg, 2) / 2 / np.power(scale, 2))\n",
    "\n",
    "def dkernel(u, v, scale):\n",
    "    ug, vg = np.meshgrid(u, v)\n",
    "    factor = (vg-ug) / np.power(scale, 2)\n",
    "    return factor * np.exp(-np.power(ug-vg, 2) / 2 / np.power(scale, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fbb4d223610>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xp = np.linspace(0, 12, 121)\n",
    "\n",
    "sigma = 2.5\n",
    "regular = 0.0001\n",
    "A = kernel(xi, xi, sigma) + regular * np.identity(xi.size)\n",
    "B = kernel(xp, xi, sigma)\n",
    "dB = dkernel(xp, xi, sigma)\n",
    "\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.imshow(A)\n",
    "plt.colorbar()\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.imshow(B)\n",
    "plt.colorbar()\n",
    "plt.subplot(3, 1, 3)\n",
    "plt.imshow(dB)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fbb4d38a0a0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MM8+YdTiOwdXX12PUqFFYvnx50PJoxm3q1KnYvXs31q9fj7fffhsfffQRZsyY0V2bYAvhxrGhoQE7duzAggULsGPHDqxduxb79u3DjTfeqNRL+DhKkowbN05mzpxppv1+v+Tm5sqSJUuS1aVzzrFjxwSAbNq0SURETp06JW63W9asWWPW2bt3rwCQ0tLSZHXTlmpra2Xo0KGyfv16mTBhgsyaNUtEOIbRmjt3rlxzzTUhywOBgOTk5Mjjjz9u5p06dUq8Xq/86U9/6o4unhOmTJkiP/7xj5W8W265RaZOnSoiHMdoAZDXXnvNTEczbnv27BEAsn37drPOunXrxDAM+frrr7ut73aij2Mw27ZtEwBy8OBBEemacUzKGZOWlhaUlZWhqKjIzHM4HCgqKkJpaWkyunROqq6uBgD07dsXAFBWVobW1lZlXIcPH468vDyOq2bmzJmYMmWKMlYAxzBab775JsaOHYsf/vCH6NevH0aPHo0XXnjBLK+oqEBlZaUyjhkZGSgoKOA4djJ+/Hhs2LABX3zxBQDgk08+webNm3H99dcD4DjGK5pxKy0tRWZmJsaOHWvWKSoqgsPhwNatW7u9z+eK6upqGIaBzMxMAF0zjnG9K+dsHT9+HH6/H9nZ2Up+dnY2Pv/882R06ZwTCAQwe/ZsXH311Rg5ciQAoLKyEh6Px/zAtMvOzkZlZWUSemlPq1evxo4dO7B9+3ZLGccwOl999RVWrFiBOXPm4Fe/+hW2b9+O+++/Hx6PByUlJeZYBTvGOY4d5s2bh5qaGgwfPhxOpxN+vx+PPvoopk6dCgAcxzhFM26VlZXo16+fUu5yudC3b1+ObQhNTU2YO3cuiouLzRf5dcU4JiUwobM3c+ZM7Nq1C5s3b052V84phw8fxqxZs7B+/Xr4fL5kd+ecFQgEMHbsWPz2t78FAIwePRq7du3Cc889h5KSkiT37tzx6quv4uWXX8Yf//hHjBgxAjt37sTs2bORm5vLcSRbaW1txa233goRwYoVK7p0XUm5lJOVlQWn02m506Gqqgo5OTnJ6NI55b777sPbb7+NjRs3YsCAAWZ+Tk4OWlpacOrUKaU+x7VDWVkZjh07hiuvvBIulwsulwubNm3C008/DZfLhezsbI5hFPr3749vf/vbSt5ll12GQ4cOAYA5VjzGw3vwwQcxb9483H777cjPz8e0adPwwAMPYMmSJQA4jvGKZtxycnIsN1u0tbXh5MmTHFtNe1By8OBBrF+/3jxbAnTNOCYlMPF4PBgzZgw2bNhg5gUCAWzYsAGFhYXJ6NI5QURw33334bXXXsMHH3yAwYMHK+VjxoyB2+1WxnXfvn04dOgQx/WMiRMn4rPPPsPOnTvNn7Fjx2Lq1KnmvzmGkV199dWWW9W/+OILDBo0CAAwePBg5OTkKONYU1ODrVu3chw7aWhogMOhfg07nU4EAgEAHMd4RTNuhYWFOHXqFMrKysw6H3zwAQKBAAoKCrq9z3bVHpTs378f77//Pi644AKlvEvGMa4pswmwevVq8Xq9smrVKtmzZ4/MmDFDMjMzpbKyMlldsr2f/vSnkpGRIR9++KF888035k9DQ4NZ595775W8vDz54IMP5OOPP5bCwkIpLCxMYq/tr/NdOSIcw2hs27ZNXC6XPProo7J//355+eWXJTU1Vf7whz+YdZYuXSqZmZnyxhtvyKeffio33XSTDB48WBobG5PYc3spKSmRb33rW/L2229LRUWFrF27VrKysuShhx4y63Acg6utrZXy8nIpLy8XAPLkk09KeXm5ebdINOM2efJkGT16tGzdulU2b94sQ4cOleLi4mRtUlKEG8eWlha58cYbZcCAAbJz507l705zc7PZRqLHMWmBiYjIM888I3l5eeLxeGTcuHGyZcuWZHbH9gAE/Vm5cqVZp7GxUX72s59Jnz59JDU1Vb7//e/LN998k7xOnwP0wIRjGJ233npLRo4cKV6vV4YPHy6///3vlfJAICALFiyQ7Oxs8Xq9MnHiRNm3b1+SemtPNTU1MmvWLMnLyxOfzydDhgyRX//618qXPscxuI0bNwb9PiwpKRGR6MbtxIkTUlxcLL1795b09HS5++67pba2NglbkzzhxrGioiLk352NGzeabSR6HA2RTo8YJCIiIkoiviuHiIiIbIOBCREREdlG0p5j0tTUhJaWlmStnoiIiOLg8Xi69DlQSQlMmpqakJHSBy3o2S+hIiIiOtfk5OSgoqKiy4KTpAQmLS0taEETrsH34DK8AADDYeDMP7T0md9a2mi/998s75Rur3OmLX3ZoMsAwJlfodaJUO2hU1orE7MtrW0j2npQy7U+KvnteQ69ToQ2HcHXoS9nzpJuz3d0aj/UMtoQRSx3hK9v6lxuqRsqHWr7Ii0XIh2ujlYebdux5FvqIMSyofKjXrdY8yP001wGGstyEqFPYl1OyzMitQW9vtorI0J7hvk72LpFXWXnup1+OyxtSdhyB6ztmmV6XX0ZPT/E747DOEJ9SKe8gNaGuu72cqcRPL/969Fp9lVtr2O5jnwn9DoBZd1Os40z6za3qz2t9UFvDwG1nU7tmnUBpW5H2/r26m1Z21T6FCLf6LTdHf0XJd2RD6Uts6/mWBtafns6+G+nYcBxpnZHXke6pjaAQWP+jpaWlvMrMOlYuRsuww0AMLQ//npaP9INS36ntEOrE3VgYvk2Cb6OUO11SWASvrxbAxP9Cz8JgUnQ9qL8o5/wwCTcuhFf22cVmIRaFrGtK6GBidYHWwUmIdNqe52DiFDLdnxMows8og5MOpUnOjBxIPp6oQITaxuRAhP9j2r8gYn+Rz1UIGJNxx6YOM26xpllDSXd0e/2tFre0WZ7vh7IQOurmAFWtIGJM87ApKO8o++hA5PumZbKya9ERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbhSubK29AKyOnYyBDjTK6ePvNbSxvi0Mo7pQNn6hhaHUP73R6XmfnQyvXlQrTXOS1qmbTXEa1tI9p6UMsDCL6c0SnPodeJ0KZDS1uG3FC6Zo6To1P7oZYJuRtDlOu71bJPgpQH/4gESYfavkjLhUiHq6OVR9t2LPmWOgixbKj8qNct1vwI/TSXgcaynETok1iX0/KMSG1Br6/2yojQnmH+DrZuUVfZuW6n32JpS8KWC9R2A4aYZQ6tbnvagRD5IX53HMYR6kM65QW0NtR1t5c7jeD5Z74y4DT7qrbXsVxHvhN6nYCybqfZxpl1m9vVntb6oLeHgNpOp3bNuoBSt6NtfXv1tqxtKn0KkW902u6O/ouS7siH0pbZV3OsDS2/PR38t9MwzLodeR3rqKlt/yPUdZISmHg8HuTk5GBz5Tsd31z+ZPSEiIiIYpGTkwOPx9Nl7RsiYvlPTXdoampCS0tLMlbd49TU1GDgwIE4fPgw0tPTk90d0nD/2Bv3j71x/3Q/j8cDn8/XZe0n7VKOz+fr0g0jq/T0dB64Nsb9Y2/cP/bG/XP+4ORXIiIisg0GJkRERGQbDEx6AK/Xi0WLFsHr9Sa7KxQE94+9cf/YG/fP+Sdpk1+JiIiIdDxjQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBibnqZMnT2Lq1KlIT09HZmYmpk+fjrq6urDLfPe734VhGMrPvffe2009Pr8tX74cF110EXw+HwoKCrBt27aw9desWYPhw4fD5/MhPz8f77zzTjf1tGeKZf+sWrXKcpzwYZFd56OPPsINN9yA3NxcGIaB119/PeIyH374Ia688kp4vV5ccsklWLVqVZf3kxKHgcl5aurUqdi9ezfWr1+Pt99+Gx999BFmzJgRcbl77rkH33zzjfnz2GOPdUNvz2+vvPIK5syZg0WLFmHHjh0YNWoUJk2ahGPHjgWt/3//938oLi7G9OnTUV5ejptvvhk333wzdu3a1c097xli3T/A6aeMdj5ODh482I097lnq6+sxatQoLF++PKr6FRUVmDJlCv71X/8VO3fuxOzZs/Ef//EfeO+997q4p5QwQuedPXv2CADZvn27mbdu3ToxDEO+/vrrkMtNmDBBZs2a1Q097FnGjRsnM2fONNN+v19yc3NlyZIlQevfeuutMmXKFCWvoKBAfvKTn3RpP3uqWPfPypUrJSMjo5t6R50BkNdeey1snYceekhGjBih5N12220yadKkLuwZJRLPmJyHSktLkZmZibFjx5p5RUVFcDgc2Lp1a9hlX375ZWRlZWHkyJGYP38+Ghoaurq757WWlhaUlZWhqKjIzHM4HCgqKkJpaWnQZUpLS5X6ADBp0qSQ9Sl+8ewfAKirq8OgQYMwcOBA3HTTTdi9e3d3dJeiwOPn3Je0l/hR16msrES/fv2UPJfLhb59+6KysjLkcnfccQcGDRqE3NxcfPrpp5g7dy727duHtWvXdnWXz1vHjx+H3+9Hdna2kp+dnY3PP/886DKVlZVB64fbdxSfePbPsGHD8NJLL+Hyyy9HdXU1nnjiCYwfPx67d+/GgAEDuqPbFEao46empgaNjY1ISUlJUs8oWgxMziHz5s3DsmXLwtbZu3dv3O13noOSn5+P/v37Y+LEifjyyy9x8cUXx90u0fmksLAQhYWFZnr8+PG47LLL8Pzzz+ORRx5JYs+Izg8MTM4hv/jFL3DXXXeFrTNkyBDk5ORYJu61tbXh5MmTyMnJiXp9BQUFAIADBw4wMIlTVlYWnE4nqqqqlPyqqqqQ+yInJyem+hS/ePaPzu12Y/To0Thw4EBXdJFiFOr4SU9P59mScwTnmJxDLrzwQgwfPjzsj8fjQWFhIU6dOoWysjJz2Q8++ACBQMAMNqKxc+dOAED//v0TvSk9hsfjwZgxY7BhwwYzLxAIYMOGDcr/ujsrLCxU6gPA+vXrQ9an+MWzf3R+vx+fffYZjxOb4PFzHkj27FvqGpMnT5bRo0fL1q1bZfPmzTJ06FApLi42y48cOSLDhg2TrVu3iojIgQMH5OGHH5aPP/5YKioq5I033pAhQ4bItddem6xNOG+sXr1avF6vrFq1Svbs2SMzZsyQzMxMqaysFBGRadOmybx588z6f/vb38TlcskTTzwhe/fulUWLFonb7ZbPPvssWZtwXot1/yxevFjee+89+fLLL6WsrExuv/128fl8snv37mRtwnmttrZWysvLpby8XADIk08+KeXl5XLw4EEREZk3b55MmzbNrP/VV19JamqqPPjgg7J3715Zvny5OJ1Oeffdd5O1CRQjBibnqRMnTkhxcbH07t1b0tPT5e6775ba2lqzvKKiQgDIxo0bRUTk0KFDcu2110rfvn3F6/XKJZdcIg8++KBUV1cnaQvOL88884zk5eWJx+ORcePGyZYtW8yyCRMmSElJiVL/1VdflUsvvVQ8Ho+MGDFC/vKXv3Rzj3uWWPbP7NmzzbrZ2dnyve99T3bs2JGEXvcMGzduFACWn/Z9UlJSIhMmTLAsc8UVV4jH45EhQ4bIypUru73fFD9DRCSJJ2yIiIiITJxjQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi22BgQkRERLbBwISIiIhsg4EJERER2QYDEyIiIrINBiZERERkGwxMiIiIyDYYmBAREZFtnFVgsnz5clx00UXw+XwoKCjAtm3bEtUvIiIi6oEMEZF4FnzllVdw55134rnnnkNBQQGeeuoprFmzBvv27UO/fv3CLhsIBHD06FGkpaXBMIy4Ok5ERETdS0RQW1uL3NxcOBxdc9El7sCkoKAAV111FZ599lkAp4ONgQMH4uc//znmzZsXdtkjR45g4MCB8ayWiIiIkuzw4cMYMGBAl7TtimehlpYWlJWVYf78+Waew+FAUVERSktLLfWbm5vR3NxspttjoWE/Xginx3d6+TY1PnK0Iny6zRpPGf7wdSKlEdCWD6jlhl+rryWNOGI80c8YGXq5lnaqGeIInw64tXKntQ8BV/g6enlA+9QE3FraqfdBLRd9+WB90pdxamOr91FL69ugLy96oG8pD7Iv9ZN7lrT+gbA2cVb0LukfjqiWUZNGQP+AafW1cssaLe1F0wetzQh9tKQjiGfYI64iUqMRjttIn42guzLC5y1yn2P8PNrh5HU8+17/PMXYZuTPX+I/r7H20bJ8XKcTIqwjyv0faG7C35c9grS0tAR0Iri4ApPjx4/D7/cjOztbyc/Ozsbnn39uqb9kyRIsXrzYku/0+OD0nglMtD8E2t9XazrIHw5Hm76M3mb4tCUw0QIRQ69vh8AkQqAST2CiBx6GVm7o5VoQYakfITAxgvTJuowWOOjLxBqYWJZnYBK0vh6YRGwvmj4wMElIYBKxTz00MInx88TApL3R2BbvymkYcQUmsZo/fz7mzJljpmtqajBw4EA8fO8q9Eo7/Rci09mgLJNmqKdI0hzqN14vw3pty6v9xXRrf/H0dCR+UdfZBvWUTKuo6QYtDQC12lmXWu1UwKlAipI+4e+tpP/Rpkalx7X0sRatvFld/kRTLyVd3eyz9rHRq6SbGj1KOlCvjqvRpI6jq1H9gGq7Es5mNe1qVNOeJutRZlmmWT+jpqadLVoQqZ8d04NMrTwRQaV+FkZcaoblTJQWNPrd4YNKS7m6m07X8YSv49fSlrNdHtHSWrkWIFrObHms42g52+XSohet3NDTWpBo+T7UvqWj2pPaHxvtUIfof/W1AE384cthKVeThlaup0/nhV/G0qYlbcRUHtcfWP3/arEGP3oXtH1tOaaCTWmIUCfSf0oC+n9CLP+p0f/HqteX8OWI4jNt+Y95pGMg/DFh+U90ArQfE9LQlPC2dXEFJllZWXA6naiqqlLyq6qqkJOTY6nv9Xrh9Xot+URERESdxTWl1uPxYMyYMdiwYYOZFwgEsGHDBhQWFiasc0RERNSzxH0pZ86cOSgpKcHYsWMxbtw4PPXUU6ivr8fdd9+dyP4RERFRDxJ3YHLbbbfhH//4BxYuXIjKykpcccUVePfddy0TYsN5+qe3wuU6PedBv+PF0Wa56Bs+HYxlDoA+EVSbA6DNCQi4tbRHL1fba/NZL7D6vVodLe3XlmlTp5zAr00J8aeo292mpQMp6rgZKeqFapdPu70JQIqW1z+rWkmnf0u9ppjpaQybTnOp9dOcarq3lvYZ1j75tNuwHNoFdad2DdWvXdxu1WbYNok6GaJBmzzR4FcvNda0WefinGpNVdLVrWqdfzar5XXNapv1Teo6LXN5GrS5PI3qxW6nNjdHn9tzOk9N68v46rS5OdrlYn0uj7NZHXeHNpfH2aKV68ctAOjzewL6sazVt8xDiDTB26mltfquYMeleizrc3Msae1KtH6s6+WWuT0+7fOqz93xWr/PAtoy4laPZcOjjb1bSzvV+k5tbo9TmzsR8eYAWOcu6HNxAvrcHW15v98RNh2IVN4a5CS/ntemza3Ryh0t2pw4rb5eHvEOUcsdo9Yu6nPi9DqGfuOGPr/IcoeoVh7rBN8grBO2g5f7W2ObqxmPs5r8et999+G+++5LVF+IiIioh+O7coiIiMg2GJgQERGRbXTLc0xC8S08Bnev0xdbHdCvb4a//hmMfn0zoN3QHtAumrX41WtlftGvb6rlzVq6pU1PW4ezTavTpl2f82vXP0W/Xqqljdbw10Pd1Wr7xnE17Wi13rbdpl0jrdauX9Zo6a8tz1fQ0rE+gCiKh0tZn02gpi1Po9XS+kPd/PrzOiI8zwMARJsHIPo1fp96odjlUQfG61UHut8FNUq6d/8WJd3LpaZ7u9WHu6S7rc8TSHGoy6Q41XWmauVu7WK3M8JxqB9TrdqO0NMA0KBNqKjTJmTUt6lpfe5ObYue1pZvDj93p7VR27kADG3ujSPC3BxXg/qBtDyLpzb83B13Y/i5O84m69wcy/yeVm3+WKs258SvlVueVK1PPNDmg+jPhnJZ/98a0J/No8278+vz8rS5PG0+PR1+np4/JfwcPMA6D68tVZvPo8/vSVPHLZCiHgNu7Tj2+rTj0qsdlx7tuPRYj8sM7Vjt5VKX6a09uEk/TlO1crf2paunnfpDboLwa+cl9L+f+ry85jNfkk11rShbE7H5s8IzJkRERGQbDEyIiIjINhiYEBERkW0wMCEiIiLbSOrk10N/uch8u3AXvHMo6gfGmCK9DCrGCZnB2nRYXlgWY5v6S660PdjmVSc9WV6gFiwU1Qdfr6O/lCrSm1P1Yn3c4nhjaKS33lrmeulvBI35pWrWLjnqtYnItVrarz0gTWujVeuzPsm4Wu9TAh6apIv0krVInz9LWn+pX5BjwFJHf/Gf9mAwuLVjRJtE7NTquz3qZMVeqepEQV9mnaVPqW51UnCKS5sk7Ao/EVmfVOzRJhF7tbRlcmLQ1zCHp0/Ob9ZmeOvpRm3ScX2b9lBBLV2rTYyvb7G+JTLSROM27eWbsLzgU0s3aZOK6yNMMq62fuhdlWra3aCOrUtLuxu0Cd9a2tGg7mujUduoZrVcmtXyWq0cAGpatCeoace++PXZ+vqBFGTWb2cO7aYHp5Z2W//UGx7tQNTeZ2d41H0rvtPpNn8zgPfD9+cs8YwJERER2UZcgclvfvMbGIah/AwfPjzRfSMiIqIeJu5LOSNGjMD773ecznG5knpViIiIiM4DcUcTLpcLOTk5Z7Xyukva4EgJ8sajYPQL6pEulidCxGv8UfQh1oeN6XMjItXXLlU79LkUlrkakfsccZ3JEGluRIzzXiLNN9LnWgDW+ToR1xlhjlOkPlnWH8ekkqg+o8pKYk1H+LwC1s+ofsjrDxHU5w9pE6n0dbRFSDcE6dPJrv6MR5rfpn++guwmy2dS//xZ5v9oGxGxXEu7wr8UELC++M+lvVgwRZvf485Sy31uded7tBcNep1quU9Pu6wv/NTn9+jzf9zafB6v9tY9l0N72B3CP9wzEfOD9IeZ6Q8mbNYmYrXp5X59PpFav0krb/JbHzKot9GkPSC0qVVNtz9A1N9gAHdYmkuouOeY7N+/H7m5uRgyZAimTp2KQ4cOhazb3NyMmpoa5YeIiIhIF1dgUlBQgFWrVuHdd9/FihUrUFFRge985zuora0NWn/JkiXIyMgwfwYOHHhWnSYiIqLzkyES1c2bYZ06dQqDBg3Ck08+ienTp1vKm5ub0dzplqrq6mrk5eUhd+mv4PD5LPVD9FRN95RLOTH3Kbb2g+GlnBDri3AHMy/lhNiEWG+DtlzKiW35qG6rPh8v5ei39Z/tpRxX5Es5eh23dmnHrV+qccV2KcerlUdzKcfn0C/lqNvpOQcu5bRot3636beK65dhAuEv5ej1g7ahXcppbgt1KacZB/7jKZw6dQoZGRmWdhMhITNWMzMzcemll+LAgQNBy71eL7yd7pFuv5RzdN5vE7F6IiIi6ka1tbX2Dkzq6urw5ZdfYtq0aVHVz83NxeHDhyEiyMvLw+HDh5Genp6IrvRINTU1GDhwIMfxLHEcE4PjmBgcx8TgOCZG+zgeOnQIhmEgNze3y9YVV2Dyy1/+EjfccAMGDRqEo0ePYtGiRXA6nSguLo5qeYfDgQEDBphnTtLT0/mBSQCOY2JwHBOD45gYHMfE4DgmRkZGRpePY1yByZEjR1BcXIwTJ07gwgsvxDXXXIMtW7bgwgsvTHT/iIiIqAeJKzBZvXp1ovtBRERElNx35Xi9XixatEiZGEux4zgmBscxMTiOicFxTAyOY2J05zgm5HZhIiIiokTg24WJiIjINhiYEBERkW0wMCEiIiLbYGBCREREtpHUwGT58uW46KKL4PP5UFBQgG3btiWzO7a3ZMkSXHXVVUhLS0O/fv1w8803Y9++fUqdpqYmzJw5ExdccAF69+6NH/zgB6iqqkpSj+1v6dKlMAwDs2fPNvM4htH5+uuv8aMf/QgXXHABUlJSkJ+fj48//tgsFxEsXLgQ/fv3R0pKCoqKirB///4k9th+/H4/FixYgMGDByMlJQUXX3wxHnnkEXS+J4HjGNxHH32EG264Abm5uTAMA6+//rpSHs24nTx5ElOnTkV6ejoyMzMxffp01NXVdeNWJF+4cWxtbcXcuXORn5+PXr16ITc3F3feeSeOHj2qtJHocUxaYPLKK69gzpw5WLRoEXbs2IFRo0Zh0qRJOHbsWLK6ZHubNm3CzJkzsWXLFqxfvx6tra247rrrUF9fb9Z54IEH8NZbb2HNmjXYtGkTjh49iltuuSWJvbav7du34/nnn8fll1+u5HMMI/vnP/+Jq6++Gm63G+vWrcOePXvwu9/9Dn369DHrPPbYY3j66afx3HPPYevWrejVqxcmTZqEpqamJPbcXpYtW4YVK1bg2Wefxd69e7Fs2TI89thjeOaZZ8w6HMfg6uvrMWrUKCxfvjxoeTTjNnXqVOzevRvr16/H22+/jY8++ggzZszork2whXDj2NDQgB07dmDBggXYsWMH1q5di3379uHGG29U6iV8HCVJxo0bJzNnzjTTfr9fcnNzZcmSJcnq0jnn2LFjAkA2bdokIiKnTp0St9sta9asMevs3btXAEhpaWmyumlLtbW1MnToUFm/fr1MmDBBZs2aJSIcw2jNnTtXrrnmmpDlgUBAcnJy5PHHHzfzTp06JV6vV/70pz91RxfPCVOmTJEf//jHSt4tt9wiU6dOFRGOY7QAyGuvvWamoxm3PXv2CADZvn27WWfdunViGIZ8/fXX3dZ3O9HHMZht27YJADl48KCIdM04JuWMSUtLC8rKylBUVGTmORwOFBUVobS0NBldOidVV1cDAPr27QsAKCsrQ2trqzKuw4cPR15eHsdVM3PmTEyZMkUZK4BjGK0333wTY8eOxQ9/+EP069cPo0ePxgsvvGCWV1RUoLKyUhnHjIwMFBQUcBw7GT9+PDZs2IAvvvgCAPDJJ59g8+bNuP766wFwHOMVzbiVlpYiMzMTY8eONesUFRXB4XBg69at3d7nc0V1dTUMw0BmZiaArhnHhLxdOFbHjx+H3+9Hdna2kp+dnY3PP/88GV065wQCAcyePRtXX301Ro4cCQCorKyEx+MxPzDtsrOzUVlZmYRe2tPq1auxY8cObN++3VLGMYzOV199hRUrVmDOnDn41a9+he3bt+P++++Hx+NBSUmJOVbBjnGOY4d58+ahpqYGw4cPh9PphN/vx6OPPoqpU6cCAMcxTtGMW2VlJfr166eUu1wu9O3bl2MbQlNTE+bOnYvi4mLzRX5dMY5JCUzo7M2cORO7du3C5s2bk92Vc8rhw4cxa9YsrF+/Hj6fL9ndOWcFAgGMHTsWv/3tbwEAo0ePxq5du/Dcc8+hpKQkyb07d7z66qt4+eWX8cc//hEjRozAzp07MXv2bOTm5nIcyVZaW1tx6623QkSwYsWKLl1XUi7lZGVlwel0Wu50qKqqQk5OTjK6dE6577778Pbbb2Pjxo0YMGCAmZ+Tk4OWlhacOnVKqc9x7VBWVoZjx47hyiuvhMvlgsvlwqZNm/D000/D5XIhOzubYxiF/v3749vf/raSd9lll+HQoUMAYI4Vj/HwHnzwQcybNw+333478vPzMW3aNDzwwANYsmQJAI5jvKIZt5ycHMvNFm1tbTh58iTHVtMelBw8eBDr1683z5YAXTOOSQlMPB4PxowZgw0bNph5gUAAGzZsQGFhYTK6dE4QEdx333147bXX8MEHH2Dw4MFK+ZgxY+B2u5Vx3bdvHw4dOsRxPWPixIn47LPPsHPnTvNn7NixmDp1qvlvjmFkV199teVW9S+++AKDBg0CAAwePBg5OTnKONbU1GDr1q0cx04aGhrgcKhfw06nE4FAAADHMV7RjFthYSFOnTqFsrIys84HH3yAQCCAgoKCbu+zXbUHJfv378f777+PCy64QCnvknGMa8psAqxevVq8Xq+sWrVK9uzZIzNmzJDMzEyprKxMVpds76c//alkZGTIhx9+KN98843509DQYNa59957JS8vTz744AP5+OOPpbCwUAoLC5PYa/vrfFeOCMcwGtu2bROXyyWPPvqo7N+/X15++WVJTU2VP/zhD2adpUuXSmZmprzxxhvy6aefyk033SSDBw+WxsbGJPbcXkpKSuRb3/qWvP3221JRUSFr166VrKwseeihh8w6HMfgamtrpby8XMrLywWAPPnkk1JeXm7eLRLNuE2ePFlGjx4tW7dulc2bN8vQoUOluLg4WZuUFOHGsaWlRW688UYZMGCA7Ny5U/m709zcbLaR6HFMWmAiIvLMM89IXl6eeDweGTdunGzZsiWZ3bE9AEF/Vq5cadZpbGyUn/3sZ9KnTx9JTU2V73//+/LNN98kr9PnAD0w4RhG56233pKRI0eK1+uV4cOHy+9//3ulPBAIyIIFCyQ7O1u8Xq9MnDhR9u3bl6Te2lNNTY3MmjVL8vLyxOfzyZAhQ+TXv/618qXPcQxu48aNQb8PS0pKRCS6cTtx4oQUFxdL7969JT09Xe6++26pra1NwtYkT7hxrKioCPl3Z+PGjWYbiR5HQ6TTIwaJiIiIkojvyiEiIiLbYGBCREREtpG055g0NTWhpaUlWasnIiKiOHg8ni59DlRSApOmpiZkpPRBC3r2S6iIiIjONTk5OaioqOiy4CQpgUlLSwta0IRr8D24DC8AwHAYOPMPLX3mt5Y22u/9N8s7pdvrnGlLXzboMgBw5leodSJUe+iU1srEbEtr24i2HtRyrY9KfnueQ68ToU1H8HXoy5mzpNvzHZ3aD7WMNkQRyx3h65s6l1vqhkqH2r5Iy4VIh6ujlUfbdiz5ljoIsWyo/KjXLdb8CP00l4HGspxE6JNYl9PyjEhtQa+v9sqI0J5h/g62blFX2blup98OS1sSttwBa7tmmV5XX0bPD/G74zCOUB/SKS+gtaGuu73caQTPb/96dJp9VdvrWK4j3wm9TkBZt9Ns48y6ze1qT2t90NtDQG2nU7tmXUCp29G2vr16W9Y2lT6FyDc6bXdH/0VJd+RDacvsqznWhpbfng7+22kYcJyp3ZHXka6pDWDQmL+jpaXl/ApMOlbuhstwAwAM7Y+/ntaPdMOS3ynt0OpEHZhYvk2CryNUe10SmIQv79bARP/CT0JgErS9KP/oJzwwCbduxNf2WQUmoZZFbOtKaGCi9cFWgUnItNpe5yAi1LIdH9PoAo+oA5NO5YkOTByIvl6owMTaRqTARP+jGn9gov9RDxWIWNOxByZOs65xZllDSXf0uz2tlne02Z6vBzLQ+ipmgBVtYOKMMzDpKO/oe+jApHumpXLyKxEREdkGAxMiIiKyDQYmREREZBsMTIiIiMg2GJgQERGRbTAwISIiIttgYEJERES2wcCEiIiIbIOBCREREdkGAxMiIiKyDQYmREREZBsMTIiIiMg2GJgQERGRbTAwISIiIttgYEJERES2wcCEiIiIbIOBCREREdkGAxMiIiKyDQYmREREZBsMTIiIiMg2GJgQERGRbbiSufI2tAJyOjYyxDiTq6fP/NbShji08k7pwJk6hlbH0H63x2VmPrRyfbkQ7XVOi1om7XVEa9uIth7U8gCCL2d0ynPodSK06dDSliE3lK6Z4+To1H6oZULuxhDl+m617JMg5cE/IkHSobYv0nIh0uHqaOXRth1LvqUOQiwbKj/qdYs1P0I/zWWgsSwnEfok1uW0PCNSW9Drq70yIrRnmL+DrVvUVXau2+m3WNqSsOUCtd2AIWaZQ6vbnnYgRH6I3x2HcYT6kE55Aa0Ndd3t5U4jeP6Zrww4zb6q7XUs15HvhF4noKzbabZxZt3mdrWntT7o7SGgttOpXbMuoNTtaFvfXr0ta5tKn0LkG522u6P/oqQ78qG0ZfbVHGtDy29PB//tNAyzbkdexzpqatv/CHWdpAQmHo8HOTk52Fz5Tsc3lz8ZPSEiIqJY5OTkwOPxdFn7hohY/lPTHY4dO4bs7GwcPnwY6enpyehCUtTU1GDgwIHc7h6gJ24zwO3mdvcMPXG727e5qqoK/fr167L1JO1Sjs/nAwCkp6f3mJ3aGbe75+iJ2wxwu3sabnfP0f73u6tw8isRERHZBgMTIiIiso2kBSZerxeLFi2C1+tNVheSgtvdc7a7J24zwO3mdvcMPXG7u2ubkzb5lYiIiEjHSzlERERkGwxMiIiIyDYYmBAREZFtMDAhIiIi2+iywOTRRx/F+PHjkZqaiszMzKiWEREsXLgQ/fv3R0pKCoqKirB//36lzsmTJzF16lSkp6cjMzMT06dPR11dXRdsQXxi7d/f//53GIYR9GfNmjVmvWDlq1ev7o5Niko8++W73/2uZZvuvfdepc6hQ4cwZcoUpKamol+/fnjwwQfR1tbWlZsSk1i3++TJk/j5z3+OYcOGISUlBXl5ebj//vtRXV2t1LPb/l6+fDkuuugi+Hw+FBQUYNu2bWHrr1mzBsOHD4fP50N+fj7eeecdpTyaY90OYtnuF154Ad/5znfQp08f9OnTB0VFRZb6d911l2W/Tp48uas3IyaxbPOqVass26M/fOt83NfBvrsMw8CUKVPMOnbf1x999BFuuOEG5ObmwjAMvP766xGX+fDDD3HllVfC6/XikksuwapVqyx1Yv2uCEq6yMKFC+XJJ5+UOXPmSEZGRlTLLF26VDIyMuT111+XTz75RG688UYZPHiwNDY2mnUmT54so0aNki1btsj//u//yiWXXCLFxcVdtBWxi7V/bW1t8s033yg/ixcvlt69e0ttba1ZD4CsXLlSqdd5XJItnv0yYcIEueeee5Rtqq6uNsvb2tpk5MiRUlRUJOXl5fLOO+9IVlaWzJ8/v6s3J2qxbvdnn30mt9xyi7z55pty4MAB2bBhgwwdOlR+8IMfKPXstL9Xr14tHo9HXnrpJdm9e7fcc889kpmZKVVVVUHr/+1vfxOn0ymPPfaY7NmzR/7f//t/4na75bPPPjPrRHOsJ1us233HHXfI8uXLpby8XPbu3St33XWXZGRkyJEjR8w6JSUlMnnyZGW/njx5srs2KaJYt3nlypWSnp6ubE9lZaVS53zc1ydOnFC2edeuXeJ0OmXlypVmHbvv63feeUd+/etfy9q1awWAvPbaa2Hrf/XVV5Kamipz5syRPXv2yDPPPCNOp1Peffdds06s4xhKlwUm7VauXBlVYBIIBCQnJ0cef/xxM+/UqVPi9XrlT3/6k4iI7NmzRwDI9u3bzTrr1q0TwzDk66+/TnjfY5Wo/l1xxRXy4x//WMmL5oOTLPFu94QJE2TWrFkhy9955x1xOBzKF92KFSskPT1dmpubE9L3s5Go/f3qq6+Kx+OR1tZWM89O+3vcuHEyc+ZMM+33+yU3N1eWLFkStP6tt94qU6ZMUfIKCgrkJz/5iYhEd6zbQazbrWtra5O0tDT5n//5HzOvpKREbrrppkR3NWFi3eZI3+89ZV//13/9l6SlpUldXZ2ZZ/d93Vk03zcPPfSQjBgxQsm77bbbZNKkSWb6bMexnW3mmFRUVKCyshJFRUVmXkZGBgoKClBaWgoAKC0tRWZmJsaOHWvWKSoqgsPhwNatW7u9z7pE9K+srAw7d+7E9OnTLWUzZ85EVlYWxo0bh5deeglik0fQnM12v/zyy8jKysLIkSMxf/58NDQ0KO3m5+cjOzvbzJs0aRJqamqwe/fuxG9IjBL1eayurkZ6ejpcLvXVVXbY3y0tLSgrK1OOS4fDgaKiIvO41JWWlir1gdP7rb1+NMd6ssWz3bqGhga0traib9++Sv6HH36Ifv36YdiwYfjpT3+KEydOJLTv8Yp3m+vq6jBo0CAMHDgQN910k3Js9pR9/eKLL+L2229Hr169lHy77ut4RDquEzGO7ZL2Ej9dZWUlACh/hNrT7WWVlZWWNxq6XC707dvXrJNMiejfiy++iMsuuwzjx49X8h9++GH827/9G1JTU/HXv/4VP/vZz1BXV4f7778/Yf2PV7zbfccdd2DQoEHIzc3Fp59+irlz52Lfvn1Yu3at2W6wz0N7WbIlYn8fP34cjzzyCGbMmKHk22V/Hz9+HH6/P+h++Pzzz4MuE2q/dT6O2/NC1Um2eLZbN3fuXOTm5ipf1JMnT8Ytt9yCwYMH48svv8SvfvUrXH/99SgtLYXT6UzoNsQqnm0eNmwYXnrpJVx++eWorq7GE088gfHjx2P37t0YMGBAj9jX27Ztw65du/Diiy8q+Xbe1/EIdVzX1NSgsbER//znP8/6mGkXU2Ayb948LFu2LGydvXv3Yvjw4TF1wu6i3e6z1djYiD/+8Y9YsGCBpaxz3ujRo1FfX4/HH3+8S/9QdfV2d/5jnJ+fj/79+2PixIn48ssvcfHFF8fd7tnqrv1dU1ODKVOm4Nvf/jZ+85vfKGXJ2N+UOEuXLsXq1avx4YcfKpNBb7/9dvPf+fn5uPzyy3HxxRfjww8/xMSJE5PR1bNSWFiIwsJCMz1+/HhcdtlleP755/HII48ksWfd58UXX0R+fj7GjRun5J9v+7o7xRSY/OIXv8Bdd90Vts6QIUPi6khOTg4AoKqqCv379zfzq6qqcMUVV5h1jh07pizX1taGkydPmst3hWi3+2z79+c//xkNDQ248847I9YtKCjAI488gubm5i57b0F3bXe7goICAMCBAwdw8cUXIycnxzKju6qqCgDO+f1dW1uLyZMnIy0tDa+99hrcbnfY+t2xv4PJysqC0+k0x71dVVVVyG3MyckJWz+aYz3Z4tnudk888QSWLl2K999/H5dffnnYukOGDEFWVhYOHDiQ9D9WZ7PN7dxuN0aPHo0DBw4AOP/3dX19PVavXo2HH3444nrstK/jEeq4Tk9PR0pKCpxO51l/fkwxzUiJQ6yTX5944gkzr7q6Oujk148//tis895779lu8mu8/ZswYYLl7oxQ/vM//1P69OkTd18TKVH7ZfPmzQJAPvnkExHpmPzaeUb3888/L+np6dLU1JS4DYhTvNtdXV0t//Iv/yITJkyQ+vr6qNaVzP09btw4ue+++8y03++Xb33rW2Env/77v/+7kldYWGiZ/BruWLeDWLdbRGTZsmWSnp4upaWlUa3j8OHDYhiGvPHGG2fd30SIZ5s7a2trk2HDhskDDzwgIuf3vhY5/ffN6/XK8ePHI67Dbvu6M0Q5+XXkyJFKXnFxsWXy69l8fsz+xFQ7BgcPHpTy8nLz1tfy8nIpLy9XboEdNmyYrF271kwvXbpUMjMz5Y033pBPP/1UbrrppqC3C48ePVq2bt0qmzdvlqFDh9ruduFw/Tty5IgMGzZMtm7dqiy3f/9+MQxD1q1bZ2nzzTfflBdeeEE+++wz2b9/v/z3f/+3pKamysKFC7t8e6IV63YfOHBAHn74Yfn444+loqJC3njjDRkyZIhce+215jLttwtfd911snPnTnn33XflwgsvtN3twrFsd3V1tRQUFEh+fr4cOHBAuZWwra1NROy3v1evXi1er1dWrVole/bskRkzZkhmZqZ5t9S0adNk3rx5Zv2//e1v4nK55IknnpC9e/fKokWLgt4uHOlYT7ZYt3vp0qXi8Xjkz3/+s7Jf27/zamtr5Ze//KWUlpZKRUWFvP/++3LllVfK0KFDbRFoi8S+zYsXL5b33ntPvvzySykrK5Pbb79dfD6f7N6926xzPu7rdtdcc43cdtttlvxzYV/X1taaf5cByJNPPinl5eVy8OBBERGZN2+eTJs2zazffrvwgw8+KHv37pXly5cHvV043DhGq8sCk5KSEgFg+dm4cWPHys88q6FdIBCQBQsWSHZ2tni9Xpk4caLs27dPaffEiRNSXFwsvXv3lvT0dLn77ruVYCfZIvWvoqLCMg4iIvPnz5eBAweK3++3tLlu3Tq54oorpHfv3tKrVy8ZNWqUPPfcc0HrJkus233o0CG59tprpW/fvuL1euWSSy6RBx98UHmOiYjI3//+d7n++uslJSVFsrKy5Be/+IVyW22yxbrdGzduDHpcAJCKigoRsef+fuaZZyQvL088Ho+MGzdOtmzZYpZNmDBBSkpKlPqvvvqqXHrppeLxeGTEiBHyl7/8RSmP5li3g1i2e9CgQUH366JFi0REpKGhQa677jq58MILxe12y6BBg+See+6J+Uu7q8WyzbNnzzbrZmdny/e+9z3ZsWOH0t75uK9FRD7//HMBIH/9618tbZ0L+zrUd1H7dpaUlMiECRMsy1xxxRXi8XhkyJAhyt/vduHGMVqGiE3uOSUiIqIezzbPMSEiIiJiYEJERES2wcCEiIiIbIOBCREREdkGAxMiIiKyDQYmREREZBsMTIiIiMg2GJgQERGRbTAwISIiIttgYEJERES2wcCEiIiIbIOBCREREdnG/wfPPWKmbZxFZwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "W = solve(A, B, assume_a='pos')\n",
    "dW = solve(A, dB, assume_a='pos')\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.imshow(W)\n",
    "plt.colorbar(orientation='horizontal')\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.imshow(dW)\n",
    "plt.colorbar(orientation='horizontal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zp = zi @ W\n",
    "dzp = zi @ dW\n",
    "\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.scatter(xi, zi)\n",
    "plt.plot(x_real, z_real)\n",
    "plt.plot(xp, zp)\n",
    "plt.legend(['samples', 'real', 'predict'])\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(x_real, dz_real)\n",
    "plt.plot(xp, dzp)\n",
    "plt.legend(['real', 'predict'])\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
